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If the positive integer x is a multiple of 3 and the positive integer
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20 Sep 2022, 07:45
20 Sep 2022, 07:45
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Question Stats:
58% (00:48) correct
41% (00:41) wrong based on 36 sessions
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If the positive integer x is a multiple of 3 and the positive integer y is a multiple of 4, then xy must be a multiple of which of the following?
I. 6
II. 9
III. 12
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
I. 6
II. 9
III. 12
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
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Re: If the positive integer x is a multiple of 3 and the positive integer
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24 Sep 2022, 05:49
24 Sep 2022, 05:49
Expert Reply
x = 3k (where k is a positive integer)
y = 4z (where z is a positive integer)
xy = 12kz = 3*2*2 kz
Now let us take a look at the options
I. 6
xy already contains a 3 and a 2 so IT MUST BE A MULTIPLE OF 6
II. 9
xy contains one 3 so if k/z contains a 3, then it can be a multiple of 9, else not. So, not certain
III. 12
xy already contains a 3 and two 2's so IT MUST BE A MULTIPLE OF 12
Answer - D
y = 4z (where z is a positive integer)
xy = 12kz = 3*2*2 kz
Now let us take a look at the options
I. 6
xy already contains a 3 and a 2 so IT MUST BE A MULTIPLE OF 6
II. 9
xy contains one 3 so if k/z contains a 3, then it can be a multiple of 9, else not. So, not certain
III. 12
xy already contains a 3 and two 2's so IT MUST BE A MULTIPLE OF 12
Answer - D
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Re: If the positive integer x is a multiple of 3 and the positive integer
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03 May 2023, 12:19
03 May 2023, 12:19
1
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧
Given that positive integer x is a multiple of 3 and the positive integer y is a multiple of 4. And we need to find xy must be a multiple of which of the following?
x is a multiple of 3
=> x = 3k (where k is an integer)
y is a multiple of 4
=> y = 4t (where t is an integer)
=> xy = 3k * 4t = 12kt
=> xy will be divisible by 12 and all factors of 12
=> 6 and 12 from the option choices
So, Answer will be D
Hope it helps!
Watch the following video to learn the basics of Factors and Multiples
Given that positive integer x is a multiple of 3 and the positive integer y is a multiple of 4. And we need to find xy must be a multiple of which of the following?
x is a multiple of 3
=> x = 3k (where k is an integer)
y is a multiple of 4
=> y = 4t (where t is an integer)
=> xy = 3k * 4t = 12kt
=> xy will be divisible by 12 and all factors of 12
=> 6 and 12 from the option choices
So, Answer will be D
Hope it helps!
Watch the following video to learn the basics of Factors and Multiples
